write a multiplication and subtraction equation that both involve a fraction and have the same solution. Solve your equations to show that the solutions are the same.
To create a multiplication and subtraction equation that involve fractions with the same solution, we can follow these steps:
Step 1: Choose two fractions.
Let's choose the fractions 3/4 and 2/3.
Step 2: Set up the multiplication equation.
Multiply the two fractions together. The result of this multiplication will be the same as the solution we want to find.
(3/4) * (2/3) = 6/12
Step 3: Set up the subtraction equation.
Subtract one of the fractions from the other. The result of this subtraction will also be the solution we are looking for.
(3/4) - (2/3) = ?
To solve this subtraction equation, we need to find a common denominator for the fractions involved. The least common denominator for 4 and 3 is 12.
Multiplying the numerators and denominators of (3/4) by 3 gives us (9/12), and multiplying the numerators and denominators of (2/3) by 4 gives us (8/12).
Now, we can rewrite the subtraction equation:
(9/12) - (8/12) = 1/12
Therefore, our multiplication equation (6/12) and subtraction equation (1/12) both have the same solution: 1/12.
In summary:
Multiplication equation: (3/4) * (2/3) = 6/12
Subtraction equation: (3/4) - (2/3) = 1/12